Page 43 - Mechatronic Systems Modelling and Simulation with HDLs

32 2 PRINCIPLES OF MODELLING AND SIMULATION

predetermined manoeuvre. His control inputs are used as the stimuli for the simula-
tion. A validation of the model cannot be achieved for certain manoeuvres because
the pilot and helicopter form a control loop in which even the smallest deviations
quickly accumulate to form large discrepancies between reality and simulation.
His measured control movements are correct only for reality. In order to achieve
a validation nevertheless, Bradley et al. propose to consider also the inverse of
the simulation. In this case the desired flight movements are predetermined. An
inverse model in the form of an ideal pilot calculates the necessary control of
the helicopter. This avoids the accumulation of faults described above. Thus the
validity of the helicopter model is demonstrated on the basis of outputs supplied
from the inputs generated using the inverse model. The criteria from the previous
section on direct validation based upon measured data, can again be applied here.

2.6 Model Simplification

In some cases the precision of some (sub)models is greater than is necessary for
the purposes of the simulation. This is not critical as long as the efficiency of the
simulation is not a problem. However, if the simulation times become too great then
it makes sense to consider the simplification of models, see for example Kort¨ um
and Troch [203] or Zeigler [435]. According to Zeigler the following strategies
can be drawn upon to achieve the simplification of a basic model:

• Omission of components, variables and/or interaction rules.
• Replacement of deterministic descriptions by stochastic descriptions.
• Coarsening the value range of variables.

• Grouping of components into blocks and combining the associated variables.
The first method assumes that not all factors are equally important for the
determination of the behaviour of a model. Typically, these factors are classified as
first and second-order effects. The behaviour of a model usually depends primarily
upon a few first-order effects, whilst the second-order effects, although numerous,
can generally be neglected without significantly detracting from the validity of
the resulting model. Here too the principle applies that the validity of a model is
always established from the point of view of the application. A further difficulty
is that the omission of components, variables or interaction rules can have side
effects for other parts of the model. For example, an eliminated variable may leave
behind gaps in various interaction rules, which each need to be carefully closed.
This process is not trivial.
The second principle is based upon the observation that in many cases a stochas-
tic formulation is significantly more simple to create than a complete deterministic
description. Thus, in the investigation of the performance of a computer, for
example, a proportionately weighted mix of instructions is used, instead of con-
sidering individual programmes and their sequence.